Optimization viewpoint on Kalman smoothing, with applications to robust and sparse estimation

In this paper, we present the optimization formulation of the Kalman filtering and smoothing problems, and use this perspective to develop a variety of extensions and applications. We first formulate classic Kalman smoothing as a least squares problem, highlight special structure, and show that the classic filtering and smoothing algorithms are equivalent to a particular algorithm for solving this problem. Once this equivalence is established, we present extensions of Kalman smoothing to systems with nonlinear process and measurement models, systems with linear and nonlinear inequality constraints, systems with outliers in the measurements or sudden changes in the state, and systems where the sparsity of the state sequence must be accounted for. All extensions preserve the computational efficiency of the classic algorithms, and most of the extensions are illustrated with numerical examples, which are part of an open source Kalman smoothing Matlab/Octave package.Comment: 46 pages, 11 figure

Assimilation of current measurements into a circulation model of Lake Michigan

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95190/1/wrcr11238.pd

A functional multiple imputation approach to incomplete longitudinal data

In designed longitudinal studies, information from the same set of subjects are collected repeatedly over time. The longitudinal measurements are often subject to missing data which impose an analytic challenge. We propose a functional multiple imputation approach modeling longitudinal response profiles as smooth curves of time under a functional mixed effects model. We develop a Gibbs sampling algorithm to draw model parameters and imputations for missing values, using a blocking technique for an increased computational efficiency. In an illustrative example, we apply a multiple imputation analysis to data from the Panel Study of Income Dynamics and the Child Development Supplement to investigate the gradient effect of family income on children's health status. Our simulation study demonstrates that this approach performs well under varying modeling assumptions on the time trajectory functions and missingness patterns. Copyright © 2011 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/83740/1/4201_ftp.pd

Validated stability-indicating spectrofluorimetric methods for the determination of ebastine in pharmaceutical preparations

Two sensitive, selective, economic, and validated spectrofluorimetric methods were developed for the determination of ebastine (EBS) in pharmaceutical preparations depending on reaction with its tertiary amino group. Method I involves condensation of the drug with mixed anhydrides (citric and acetic anhydrides) producing a product with intense fluorescence, which was measured at 496 nm after excitation at 388 nm

Genome-Wide Distribution of RNA-DNA Hybrids Identifies RNase H Targets in tRNA Genes, Retrotransposons and Mitochondria

During transcription, the nascent RNA can invade the DNA template, forming extended RNA-DNA duplexes (R-loops). Here we employ ChIP-seq in strains expressing or lacking RNase H to map targets of RNase H activity throughout the budding yeast genome. In wild-type strains, R-loops were readily detected over the 35S rDNA region, transcribed by Pol I, and over the 5S rDNA, transcribed by Pol III. In strains lacking RNase H activity, R-loops were elevated over other Pol III genes, notably tRNAs, SCR1 and U6 snRNA, and were also associated with the cDNAs of endogenous TY1 retrotransposons, which showed increased rates of mobility to the 5'-flanking regions of tRNA genes. Unexpectedly, R-loops were also associated with mitochondrial genes in the absence of RNase H1, but not of RNase H2. Finally, R-loops were detected on actively transcribed protein-coding genes in the wild-type, particularly over the second exon of spliced ribosomal protein genes